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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
31

Nonlinear System Identification and Control Applied to Selective Catalytic Reduction Systems

Tayamon, Soma January 2014 (has links)
The stringent regulations of emission levels from heavy duty vehicles create a demand for new methods for reducing harmful emissions from diesel engines. This thesis deals with the modelling of the nitrogen oxide (NOx) emissions from heavy duty vehicles using a selective catalyst as an aftertreatment system, utilising ammonia (NH3) for its reduction. The process of the selective catalytic reduction (SCR) is nonlinear, since the result of the chemical reactions involved depends on the load operating point and the temperature. The purpose of this thesis is to investigate different methods for nonlinear system identification of SCR systems with control applications in mind. The main focus of the thesis is on finding suitable techniques for effective NOx reduction without the need of over dosage of ammonia. By using data collected from a simulator together with real measured data, new black-box identification techniques are developed. Scaling and convergence properties of the proposed algorithms are analysed theoretically. Some of the resulting models are used for controller development using e.g. feedback linearisation techniques, followed by validation in a simulator environment. The benefits of nonlinear modelling and control of the SCR system are highlighted in a comparison with control based on linear models of the system. Further, a multiple model approach is investigated for simultaneous control of NOx and tailpipe ammonia. The results indicate an improvement in terms of ammonia slip reduction in comparison with models that do not take the ammonia slip into account. Another approach to NOx reduction is achieved by controlling the SCR temperature using techniques developed for LPV systems. The results indicate a reduction of the accumulated NOx.
32

Impaired reinforcement learning and Bayesian inference in psychiatric disorders : from maladaptive decision making to psychosis in schizophrenia

Valton, Vincent January 2015 (has links)
Computational modelling has been gaining an increasing amount of support from the neuroscience community as a tool to assay cognition and computational processes in the brain. Lately, scientists have started to apply computational methods from neuroscience to the study of psychiatry to gain further insight into the mechanisms leading to mental disorders. In fact, only recently has psychiatry started to move away from categorising illnesses using behavioural symptoms in an attempt for a more biologically driven diagnosis. To date, several neurobiological anomalies have been found in schizophrenia and led to a multitude of conceptual framework attempting to link the biology to the patients’ symptoms. Computational modelling can be applied to formalise these conceptual frameworks in an effort to test the validity or likelihood of each hypothesis. Recently, a novel conceptual model has been proposed to describe how positive symptoms (delusions, hallucinations and thought disorder) and cognitive symptoms (poor decision-making, i.e. “executive functioning”) might arise in schizophrenia. This framework however, has not been tested experimentally or against computational models. The focus of this thesis was to use a combination of behavioural experiments and computational models to independently assess the validity of each component that make up this framework. The first study of this thesis focused on the computational analysis of a disrupted prediction-error signalling and its implications for decision-making performances in complex tasks. Briefly, we used a reinforcement-learning model of a gambling task in rodents and disrupted the prediction-error signal known to be critical for learning. We found that this disruption can account for poor performances in decision-making due to an incorrect acquisition of the model of the world. This study illustrates how disruptions in prediction-error signalling (known to be present in schizophrenia) can lead to the acquisition of an incorrect world model which can lead to poor executive functioning or false beliefs (delusions) as seen in patients. The second study presented in this thesis addressed spatial working memory performances in chronic schizophrenia, bipolar disorder, first episode psychosis and family relatives of DISC1 translocation carriers. We build a probabilistic inference model to solve the working memory task optimally and then implemented various alterations of this model to test commonly debated hypotheses of cognitive deficiency in schizophrenia. Our goal was to find which of these hypotheses accounts best for the poor performance observed in patients. We found that while the performance at the task was significantly different for most patients groups in comparison to controls, this effect disappeared after controlling for IQ in one group. The models were nonetheless fitted to the experimental data and suggest that working memory maintenance is most likely to account for the poor performances observed in patients. We propose that the maintenance of information in working memory might have indirect implications for measures of general cognitive performance, as these rely on a correct filtering of information against distractions and cortical noise. Finally the third study presented in this thesis assessed the performance of medicated chronic schizophrenia patients in a statistical learning task of visual stimuli and measured how the acquired statistics influenced their perception. We find that patient with chronic schizophrenia appear to be unimpaired at statistical learning of visual stimuli. The acquired statistics however appear to induce less expectation-driven ‘hallucinations’ of the stimuli in the patients group than in controls. We find that this is in line with previous literature showing that patients are less susceptible to expectation-driven illusions than controls. This study highlights however the idea that perceptual processes during sensory integration diverge from this of healthy controls. In conclusion, this thesis suggests that impairments in reinforcement learning and Bayesian inference appear to be able to account for the positive and cognitive symptoms observed in schizophrenia, but that further work is required to merge these findings. Specifically, while our studies addressed individual components such as associative learning, working memory, implicit learning & perceptual inference, we cannot conclude that deficits of reinforcement learning and Bayesian inference can collectively account for symptoms in schizophrenia. We argue however that the studies presented in this thesis provided evidence that impairments of reinforcement learning and Bayesian inference are compatible with the emergence of positive and cognitive symptoms in schizophrenia.
33

Proposta de construção de um amortecedor de vibração ajustável, TVA, utilizando fluido magnetoreológico /

Mesquita Neto, Camilo. January 2008 (has links)
Resumo: Neste trabalho é apresentado uma proposta de absorvedor de vibrações ajustável tipo viga sanduíche utilizando fluido Magnetoreológico no centro. Para o desenvolvimento deste projeto foi realizada uma revisão sobre os vários tipos de absorvedores e algumas aplicações. Em seguida foi realizado um estudo sobre o comportamento do fluido magnetoreológico, mostrando como este material inteligente varia suas propriedades quando submetido a um campo magnético. O objetivo do estudo foi verificar as propriedades do sistema para realização de um futuro controle, que é realizado através da variação do campo magnético. Avaliou-se, também, a relação com a corrente elétrica, quais os parâmetros que o influenciam e como podemos produzir um campo magnético com a intensidade desejada. Para avaliar as características do sistema foi utilizado o modelo no programa Ansys, com o objetivo de se verificar o comportamento do sistema. Para encontrar as características reais do sistema foi utilizado o modelo na forma de espaço de estados modais, identificado através do método PEM, Método de Predição de Erros (do inglês Prediction Error Methods ���� PEM). Os testes experimentais foram realizados para se adquirir conhecimento do comportamento dinâmico deste tipo de fluido e, verificar se há repetibilidade nas medidas / Abstract: This work presents a proposal of a tunable vibrations absorber type sandwich beam, using the Magnetorheologic fluid in the intermediate layer. For the development of this study a revision of some types of absorber with some applications was carried out. After that, a study of the behavior of the magnetorheologic fluid was carried through, showing as this intelligent material tunable its properties when submitted to a magnetic field. The objective of this analysis was to verify the properties of the system for implementation of a future control, which is based on the variation of the magnetic field. It was realized an analysis of the relation of the electric current and the parameters that influence it, in order to produce a magnetic field with the desired intensity. The characteristics of the system were verified through a mathematical model obtained with the software Ansys. The real characteristics of the system were found through the identification method PEM, Prediction Error Methods, using modal space states formulation. Experimental tests were carried out in order to obtain know how of the dynamic behavior of this type of material / Orientador: Vicente Lopes Junior / Coorientador: Michael J. Brennan / Banca: Hermes Adolfo de Aquino / Banca: Edson Antonio Capello Sousa / Mestre
34

Complexity, Fun, and Robots

Warmke, Daniel A. 23 September 2019 (has links)
No description available.
35

The role of task relevance in the modulation of brain dynamics during sensory predictions

Greco, Antonino 01 June 2021 (has links)
Associative learning is a fundamental ability biological systems possess in order to adapt to a nonstationary environment. One of the core aspects of associative learning theoretical frameworks is that surprising events drive learning by signalling the need to update the system’s beliefs about the probability structure governing stimuli associations. Specifically, the central neural system generates internal predictions to anticipate the causes of its perceptual experience and compute a prediction error to update its generative model of the environment, an idea generally known as the predictive coding framework. However, it is not clear whether the brain generates these predictions only for goal-oriented behavior or they are more a general characteristic of the brain function. In this thesis, I explored the role of task relevance in modulating brain activity when exposed to sensory associative learning task. In the first study, participants were asked to perform a perceptual detection task while audio-visual stimuli were presented as distractors. These distractors possessed a probability structure that made some of them more paired than others. Results showed that occipital activity triggered by the conditioned stimulus was elicited just before the arrival of the unconditioned visual stimulus. Moreover, occipital activity after the onset of the unconditioned stimulus followed a pattern of precision-weighted prediction errors. In the second study, two more sessions were added to the task in the previous study in which the probability structure for all stimuli associations was identical and the whole experiment was spanned in six days across two weeks. Results showed a difference in the modulation of the beta band induced by the presentation of the unconditioned stimulus preceded by the predictive and unpredictive conditioned auditory stimuli by comparing the pre and post sessions activity. In the third study, participants were exposed to a similar task with respect to the second study with the modification that there was a condition in which the conditioned-unconditioned stimulus association was task-relevant, thus allowing to directly compare task-relevant and task-irrelevant associations. Results showed that both types of associations had similar patterns in terms of activity and functional connectivity when comparing the brain responses to the onset of the unconditioned visual stimulus. Taken together, these findings demonstrate irrelevant associations rely on the same neural mechanisms of relevant ones. Thus, even if task relevance plays a modulatory role on the strength of the neural effects of associative learning, predictive processes take place in sensory associative learning regardless of task relevance.
36

Model-Based Design, Development and Control of an Underwater Vehicle / Modellbaserad design, utveckling och reglering av ett undervattensfordon

Aili, Adam, Ekelund, Erik January 2016 (has links)
With the rising popularity of ROVs and other UV solutions, more robust and high performance controllers have become a necessity. A model of the ROV or UV can be a valuable tool during control synthesis. The main objective of this thesis was to use a model in design and development of controllers for an ROV. In this thesis, an ROV from Blue Robotics was used. The ROV was equipped with 6 thrusters placed such that the ROV was capable of moving in 6-DOFs. The ROV was further equipped with an IMU, two pressure sensors and a magnetometer. The ROV platform was further developed with EKF-based sensor fusion, a control system and manual control capabilities. To model the ROV, the framework of Fossen (2011) was used. The model was estimated using two different methods, the prediction-error method and an EKF-based method. Using the prediction-error method, it was found that the initial states of the quaternions had a large impact on the estimated parameters and the overall fit to validation data. A Kalman smoother was used to estimate the initial states. To circumvent the problems with the initial quaternions, an \abbrEKF was implemented to estimate the model parameters. The EKF estimator was less sensitive to deviations in the initial states and produced a better result than the prediction-error method. The resulting model was compared to validation data and described the angular velocities well with around 70 % fit. The estimated model was used to implement feedback linearisation which was used in conjunction with an attitude controller and an angular velocity controller. Furthermore, a depth controller was developed and tuned without the use of the model. Performance of the controllers was tested both in real tests and simulations. The angular velocity controller using feedback linearisation achieved good reference tracking. However, the attitude controller could not stabilise the system while using feedback linearisation. Both controllers' performance could be improved further by tuning the controllers' parameters during tests. The fact that the feedback linearisation made the ROV unstable, indicates that the attitude model is not good enough for use in feedback linearisation. To achieve stability, the magnitude of the parameters in the feedback linearisation were scaled down. The assumption that the ROV's center of rotation coincides with the placement of the ROV's center of gravity was presented as a possible source of error. In conclusion, good performance was achieved using the angular velocity controller. The ROV was easier to control with the angular velocity controller engaged compared to controlling it in open loop. More work is needed with the model to get acceptable performance from the attitude controller. Experiments to estimate the center of rotation and the center of gravity of the ROV may be helpful when further improving the model.
37

Enhancing fuzzy associative rule mining approaches for improving prediction accuracy : integration of fuzzy clustering, apriori and multiple support approaches to develop an associative classification rule base

Sowan, Bilal Ibrahim January 2011 (has links)
Building an accurate and reliable model for prediction for different application domains, is one of the most significant challenges in knowledge discovery and data mining. This thesis focuses on building and enhancing a generic predictive model for estimating a future value by extracting association rules (knowledge) from a quantitative database. This model is applied to several data sets obtained from different benchmark problems, and the results are evaluated through extensive experimental tests. The thesis presents an incremental development process for the prediction model with three stages. Firstly, a Knowledge Discovery (KD) model is proposed by integrating Fuzzy C-Means (FCM) with Apriori approach to extract Fuzzy Association Rules (FARs) from a database for building a Knowledge Base (KB) to predict a future value. The KD model has been tested with two road-traffic data sets. Secondly, the initial model has been further developed by including a diversification method in order to improve a reliable FARs to find out the best and representative rules. The resulting Diverse Fuzzy Rule Base (DFRB) maintains high quality and diverse FARs offering a more reliable and generic model. The model uses FCM to transform quantitative data into fuzzy ones, while a Multiple Support Apriori (MSapriori) algorithm is adapted to extract the FARs from fuzzy data. The correlation values for these FARs are calculated, and an efficient orientation for filtering FARs is performed as a post-processing method. The FARs diversity is maintained through the clustering of FARs, based on the concept of the sharing function technique used in multi-objectives optimization. The best and the most diverse FARs are obtained as the DFRB to utilise within the Fuzzy Inference System (FIS) for prediction. The third stage of development proposes a hybrid prediction model called Fuzzy Associative Classification Rule Mining (FACRM) model. This model integrates the ii improved Gustafson-Kessel (G-K) algorithm, the proposed Fuzzy Associative Classification Rules (FACR) algorithm and the proposed diversification method. The improved G-K algorithm transforms quantitative data into fuzzy data, while the FACR generate significant rules (Fuzzy Classification Association Rules (FCARs)) by employing the improved multiple support threshold, associative classification and vertical scanning format approaches. These FCARs are then filtered by calculating the correlation value and the distance between them. The advantage of the proposed FACRM model is to build a generalized prediction model, able to deal with different application domains. The validation of the FACRM model is conducted using different benchmark data sets from the University of California, Irvine (UCI) of machine learning and KEEL (Knowledge Extraction based on Evolutionary Learning) repositories, and the results of the proposed FACRM are also compared with other existing prediction models. The experimental results show that the error rate and generalization performance of the proposed model is better in the majority of data sets with respect to the commonly used models. A new method for feature selection entitled Weighting Feature Selection (WFS) is also proposed. The WFS method aims to improve the performance of FACRM model. The prediction performance is improved by minimizing the prediction error and reducing the number of generated rules. The prediction results of FACRM by employing WFS have been compared with that of FACRM and Stepwise Regression (SR) models for different data sets. The performance analysis and comparative study show that the proposed prediction model provides an effective approach that can be used within a decision support system.
38

Computational modelling of the neural systems involved in schizophrenia

Thurnham, A. J. January 2008 (has links)
The aim of this thesis is to improve our understanding of the neural systems involved in schizophrenia by suggesting possible avenues for future computational modelling in an attempt to make sense of the vast number of studies relating to the symptoms and cognitive deficits relating to the disorder. This multidisciplinary research has covered three different levels of analysis: abnormalities in the microscopic brain structure, dopamine dysfunction at a neurochemical level, and interactions between cortical and subcortical brain areas, connected by cortico-basal ganglia circuit loops; and has culminated in the production of five models that provide useful clarification in this difficult field. My thesis comprises three major relevant modelling themes. Firstly, in Chapter 3 I looked at an existing neural network model addressing the Neurodevelopmental Hypothesis of Schizophrenia by Hoffman and McGlashan (1997). However, it soon became clear that such models were overly simplistic and brittle when it came to replication. While they focused on hallucinations and connectivity in the frontal lobes they ignored other symptoms and the evidence of reductions in volume of the temporal lobes in schizophrenia. No mention was made of the considerable evidence of dysfunction of the dopamine system and associated areas, such as the basal ganglia. This led to my second line of reasoning: dopamine dysfunction. Initially I helped create a novel model of dopamine neuron firing based on the Computational Substrate for Incentive Salience by McClure, Daw and Montague (2003), incorporating temporal difference (TD) reward prediction errors (Chapter 5). I adapted this model in Chapter 6 to address the ongoing debate as to whether or not dopamine encodes uncertainty in the delay period between presentation of a conditioned stimulus and receipt of a reward, as demonstrated by sustained activation seen in single dopamine neuron recordings (Fiorillo, Tobler & Schultz 2003). An answer to this question could result in a better understanding of the nature of dopamine signaling, with implications for the psychopathology of cognitive disorders, like schizophrenia, for which dopamine is commonly regarded as having a primary role. Computational modelling enabled me to suggest that while sustained activation is common in single trials, there is the possibility that it increases with increasing probability, in which case dopamine may not be encoding uncertainty in this manner. Importantly, these predictions can be tested and verified by experimental data. My third modelling theme arose as a result of the limitations to using TD alone to account for a reinforcement learning account of action control in the brain. In Chapter 8 I introduce a dual weighted artificial neural network, originally designed by Hinton and Plaut (1987) to address the problem of catastrophic forgetting in multilayer artificial neural networks. I suggest an alternative use for a model with fast and slow weights to address the problem of arbitration between two systems of control. This novel approach is capable of combining the benefits of model free and model based learning in one simple model, without need for a homunculus and may have important implications in addressing how both goal directed and stimulus response learning may coexist. Modelling cortical-subcortical loops offers the potential of incorporating both the symptoms and cognitive deficits associated with schizophrenia by taking into account the interactions between midbrain/striatum and cortical areas.
39

Identification of rigid industrial robots - A system identification perspective / Identification de robots industriels rigides – Apport des méthodes de l’identification de systèmes

Brunot, Mathieu 30 November 2017 (has links)
L’industrie moderne fait largement appel à des robots industriels afin de réduire les coûts, ou encore améliorer la productivité et la qualité par exemple. Pour ce faire, une haute précision et une grande vitesse sont simultanément nécessaires. La conception de lois de commande conformes à de telles exigences demande une modélisation mathématique précise de ces robots. A cette fin, des modèles dynamiques sont construits à partir de données expérimentales. L’objectif de cette thèse est ainsi de fournir aux ingénieurs roboticiens des outils automatiques pour l’identification de bras robotiques. Dans cette perspective, une analyse comparative des méthodes existantes pour l’identification de robot est réalisée. Les avantages et inconvénients de chaque méthode sont ainsi mis en exergue. À partir de ces observations, les contributions sont articulées selon trois axes. Premièrement, l’étude porte sur l’estimation des vitesses et accélérations des corps du robot à partir de la position mesurée. Ces informations sont en effet nécessaires à la construction du modèle. La méthode usuelle est basée sur prétraitement "sur mesure" qui requière une connaissance fiable des bande-passantes du système, alors que celui-ci est encore inconnu. Pour surmonter ce dilemme, nous proposons une méthode capable d’estimer les dérivées automatiquement sans réglage préalable par l’utilisateur. Le deuxième axe concerne l’identification du contrôleur. Sa connaissance est en effet requise par la grande majorité des méthodes d’identification. Malheureusement, pour des raisons de propriété industrielle, il n’est pas toujours accessible. Pour traiter ce problème, deux méthodes sont introduites. Leur principe de base est d’identifier la loi de commande dans un premier temps avant d’identifier le modèle dynamique du bras robotique dans un second temps. La première méthode consiste à identifier la loi de commande de manière paramétrique, alors que la seconde fait appel à une identification non-paramétrique. Finalement, le troisième axe porte sur le réglage "sur mesure" du filtre decimate. L’identification du filtre de bruit est introduite en s’inspirant des méthodes développées par la communauté d’identification de systèmes. Ceci permet l’estimation automatique des paramètres dynamiques avec de faibles covariances tout en apportant une connaissance concernant la circulation du bruit à travers le système en boucle-fermée. Toutes les méthodes proposées sont validées sur un robot industriel à six degrés de liberté. Des perspectives sont esquissées pour de futurs travaux portant sur l’identification de systèmes robotiques, voire d’autres applications. / In modern manufacturing, industrial robots are essential components that allow saving cost, increase quality and productivity for instance. To achieve such goals, high accuracy and speed are simultaneously required. The design of control laws compliant with such requirements demands high-fidelity mathematical models of those robots. For this purpose, dynamic models are built from experimental data. The main objective of this thesis is thus to provide robotic engineers with automatic tools for identifying dynamic models of industrial robot arms. To achieve this aim, a comparative analysis of the existing methods dealing with robot identification is made. That allows discerning the advantages and the limitations of each method. From those observations, contributions are presented on three axes. First, the study focuses on the estimation of the joint velocities and accelerations from the measured position, which is required for the model construction. The usual method is based on a home-made prefiltering process that needs a reliable knowledge of the system’s bandwidths, whereas the system is still unknown. To overcome this dilemma, we propose a method able to estimate the joint derivatives automatically, without any setting from the user. The second axis is dedicated to the identification of the controller. For the vast majority of the method its knowledge is indeed required. Unfortunately, for copyright reasons, that is not always available to the user. To deal with this issue, two methods are suggested. Their basic philosophy is to identify the control law in a first step before identifying the dynamic model of the robot in a second one. The first method consists in identifying the control law in a parametric way, whereas the second one relies on a non-parametric identification. Finally, the third axis deals with the home-made setting of the decimate filter. The identification of the noise filter is introduced similarly to methods developed in the system identification community. This allows estimating automatically the dynamic parameters with low covariance and it brings some information about the noise circulation through the closed-loop system. All the proposed methodologies are validated on an industrial robot with 6 degrees of freedom. Perspectives are outlined for future developments on robotic systems identification and other complex problems.
40

Avaliação da qualidade de ajuste e predição de modelos não lineares: uma aplicação em dados de crescimento de frutos de cacaueiro / Evaluation of the quality of fit and prediction of nonlinear models: an application in growth data of cacao fruits

Eloy, Raquel Aline Oliveira 09 February 2018 (has links)
Atualmente o Brasil é o quinto maior produtor de cacau no mundo e a sua produção está diretamente ligada ao ponto certo da colheita, colher frutos verdes ou verdoengos faz com que suas sementes tenham menor peso, em 1000 frutos maduros as amêndoas secas pesam em média 40 kg, colher frutos verdoengos, ou seja, frutos que estão parcialmente maduros, faz com que esse peso caia para 36 kg em média uma perda verificada de 10%, já quando os frutos estão verdes o peso passa a ser em média de 32 kg, possuindo uma perda de 20%, por isso é importante conhecer as fases de crescimento, que permite estabelecer formas adequadas de manejo, adubação e irrigação. Dentre as características biométricas do fruto do cacaueiro as que tem maior relevância econômica são o comprimento, o diâmetro e o volume. Uma forma de explicar relações de crescimento e produtividade de plantas, árvores, frutos ou animais é por meio da utilização de modelos de crescimento, pois possuem parâmetros com interpretação biológica. Os mais utilizados nestas áreas são os modelos: Logístico, Gompertz, Von Bertalanffy, Richards e Brody, sendo os dois últimos mais utilizados para descrever o crescimento animal. O objetivo do trabalho é avaliar a qualidade de ajuste e de predição dos modelos não lineares, Logístico, Gompertz e Von Bertalanffy, para medidas de comprimento e diâmetro do fruto do cacau, com a finalidade de predizer o seu volume. Para predizer o volume do fruto foi utilizado a fórmula de volume do esferoide prolato. Os critérios AIC e BIC foram utilizados para verificar qual dos modelos se ajusta melhor à essas medidas, já para verificar qual modelo se ajusta melhor na predição do volume do fruto, foram relacionadas as estatísticas: viés médio, índice de concordância, eficiência da modelagem e o desdobramento do quadrado médio do erro de predição. / Currently Brazil is the fifth largest producer of cocoa in the world and its production is directly linked to the right point of harvest, harvesting green or green fruits makes their seeds have less weight, in 1000 mature fruits dry almonds weight on average 40 kg, harvested green fruits, that is, fruits that are partially ripe, causes this weight to fall to 36 kg on average a verified loss of 10%, when the fruits are green the weight becomes an average of 32 kg, with a loss of 20%, so it is important to know the growth phases, which allows to establish appropriate forms of management, fertilization and irrigation. Among the biometric characteristics of the cacao fruit, the most economically important are length, diameter and volume. One way to explain growth and productivity relationships of plants, trees, fruits or animals is through the use of growth models, since they have parameters that with biological interpretation are the most used in these areas: Logistics, Gompertz, Von Bertalanffy, Richards and Brody, the last two being most used to describe animal growth. The objective of this work is to evaluate the quality of fit and prediction of the non linear models, Logistic, Gompertz and Von Bertalanffy, for measures of length and diameter of the fruit of the cocoa, in order to predict its volume. To predict the volume of the fruit, the volume formula of the prolate spheroid was used. The AIC and BIC criteria were used to verify which model best fits these measures, and to verify which model best fits the fruit volume prediction, the statistics were related: mean bias, concordance index, modeling efficiency, and the unfolding of the mean square of the prediction error.

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